Problem: Express this quotient in scientific notation: ${\frac{1.600\times 10^{-6}} {2.0\times 10^{-4}}}$
Answer: Start by collecting like terms together. $= {\frac{1.600} {2.0}} \times{\frac{10^{-6}} {10^{-4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.80 \times 10^{-6\,-\,-4}$ $= 0.80 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.80$ is the same as $8.00 \div 10$ , or $8.00 \times 10^{-1}$ $ = {8.00 \times 10^{-1}} \times 10^{-2} $ $= 8.00\times 10^{-3}$